Scalar potential in F(R) supergravity

Understand

We derive a scalar potential in the recently proposed N=1 supersymmetric generalization of f(R) gravity in four space-time dimensions.

• Any such higher-derivative supergravity is classically equivalent to the standard N=1 supergravity coupled to a chiral (matter) superfield, via a Legendre-Weyl transform in superspace.
• The Kaehler potential, the superpotential and the scalar potential of that theory are all governed by a single holomorphic function.
• We also find the conditions for the vanishing cosmological constant and spontaneous supersymmetry breaking, without fine-tuning, which define a no-scale F(R) supergravity.